of Gibbs's Theory oj Surface- Concentration. 503 
from which by differentiation and comparison with the former 
we obtain 
da = — 7j s dt — Yidfii — T 2 d/jLi — etc., 
where rj s , T i9 T 2 , etc. are written for 
if ml ml 
1 ' s' 's' etC *' 
and denote the superficial densities of entropy and of the 
various substances. We may regard cr as a function of 
t-> /^i? ^2> etc., from which, if known, rj s , r 1? T 2 , may be 
determined in terms of the same variables. An equation 
between a, t, fjb x , /«t 2 , etc. may therefore be called a funda- 
mental equation for the surface of discontinuity." 
The final equation obtained above has been simplified and 
applied by Gibbs * to an actual case, viz. : — 
" If liquid mercury meet the mixed vapors of water and 
mercury in a plane surface, and we use fi ± and /jl 2 to denote the 
[chemical] potentials of mercury and water respectively and 
place the dividing surface so that I\ = 0, i. e., so that the 
total quantity of mercury is the same as if the liquid mercury 
reached this surface on one side and the mercury vapor on 
the other, without change of density on either side, then 
r a ,i will represent the amount of water in the vicinity of the 
surface above that which there ivoidd be if the water-vapor 
just reached the surface without change of density, and this 
quantity (which we may call the quantity condensed p. e., 
adsorbed] upon the mercury) will be determined by the 
equation 
dar 
d/JL 2 ' 
T2>1 — 
In this equation and the following, the temperature is 
constant and the surface of discontinuity plane. 
" If the pressures in the mixed vapors conform to the law 
of Dalton, we shall have for constant temperature 
dp 2 = cd/ju 2 ; 
p 2 denotes the part of the pressure in the vapor due to the 
water-vapor, and c the density of the water-vapor. Hence 
n _ da » 
2 ' 1- " C dp 2 
* Gibbs, ' Scientific Papers/ vol. i. p. 235. 
